A team has finished a game with 16-5 singles and extra-base hits 85 times since 1897, most recently Boston Red Sox on 10 September 2022. That is about one every 5,211 team-games.
Box score for the most recent one ↗
15-13 16-0 16-1 16-2 16-3 16-4 16-5 16-6 16-7 16-8 16-9 16-10 16-11
The whole distribution — Singles and Extra-Base Hits · All 18 shapes